The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for th
e strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)approx 2 p/(nvarepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $varepsilon=frac{hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.
Using Yang and Yangs particle-hole description, we present a thorough derivation of the thermodynamic Bethe ansatz equations for a general $SU(kappa)$ fermionic system in one-dimension for both the repulsive and attractive regimes under the presence
of an external magnetic field. These equations are derived from Sutherlands Bethe ansatz equations by using the spin-string hypothesis. The Bethe ansatz root patterns for the attractive case are discussed in detail. The relationship between the various phases of the magnetic phase diagrams and the external magnetic fields is given for the attractive case. We also give a quantitative description of the ground state energies for both strongly repulsive and strongly attractive regimes.
A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multi-component strongly attractive fermionic atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal multi-component Tomon
aga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral N-atom composites and spin-(N-1)/2 single atoms. The equation of states is also obtained to open up the study of multi-component TLL phases in 1D systems of N-component Fermi gases with population imbalance.
We investigate magnetism and quantum phase transitions in a one-dimensional system of integrable spin-1 bosons with strongly repulsive density-density interaction and antiferromagnetic spin exchange interaction via the thermodynamic Bethe ansatz meth
od. At zero temperature, the system exhibits three quantum phases: (i) a singlet phase of boson pairs when the external magnetic field $H$ is less than the lower critical field $H_{c1}$; (ii) a ferromagnetic phase of atoms in the hyperfine state $|F=1, m_{F}=1>$ when the external magnetic field exceeds the upper critical field $H_{c2}$; and (iii) a mixed phase of singlet pairs and unpaired atoms in the intermediate region $H_{c1}<H<H_{c2}$. At finite temperatures, the spin fluctuations affect the thermodynamics of the model through coupling the spin bound states to the dressed energy for the unpaired $m_{F}=1$ bosons. However, such spin dynamics is suppressed by a sufficiently strong external field at low temperatures. Thus the singlet pairs and unpaired bosons may form a two-component Luttinger liquid in the strong coupling regime.
Paired states, trions and quarteting states in one-dimensional SU(4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transitions are identified and calculated from the quarteting phase into norma
l Fermi liquid, trionic states and spin-2 paired states which belong to the universality class of linear field-dependent magnetization in the vicinity of critical points. Moreover, unified exact results for the ground state energy, chemical potentials and complete phase diagrams for isospin $S=1/2, 1, 3/2$ attractive fermions with external fields are presented. Also identified are the magnetization plateaux of $m^z=M_s/3$ and $m^z=2M_s/3$, where $M_s$ is the magnetization saturation value. The universality of finite-size corrections and collective dispersion relations provides a further test ground for low energy effective field theory.
We propose an exactly solvable model of one-dimensional anyons with competing $delta$-function and derivative $delta$-function interaction potentials. The Bethe ansatz equations are derived in terms of the $N$-particle sector for the quantum anyonic
field model of the generalized derivative nonlinear Schr{o}dinger equation. This more general anyon model exhibits richer physics than that of the recently studied one-dimensional model of $delta$-function interacting anyons. We show that the anyonic signature is inextricably related to the velocities of the colliding particles and the pairwise dynamical interaction between particles.
We investigate magnetic properties and statistical effects in 1D strongly repulsive two-component fermions and in a 1D mixture of strongly repulsive polarized fermions and bosons. Universality in the characteristics of phase transitions, magnetizatio
n and susceptibility in the presence of an external magnetic field $H$ are analyzed from the exact thermodynamic Bethe ansatz solution. We show explicitly that polarized fermions with a repulsive interaction have antiferromagnetic behavior at zero temperature. A universality class of linear field-dependent magnetization persists for weak and finite strong interaction. The system is fully polarized when the external field exceeds the critical value $H^F_capprox frac{8}{gamma}E_F$, where $E_F$ is the Fermi energy and $gamma$ is the dimensionless interaction strength. In contrast, the mixture of polarized fermions and bosons in an external field exhibits square-root field-dependent magnetization in the vicinities of H=0 and the critical value $H=H^M_capprox frac{16}{gamma}E_F$. We find that a pure boson phase occurs in the absence of the external field, fully-polarized fermions and bosons coexist for $0<H<H^M_c$, and a fully-polarized fermion phase occurs for $Hge H_c^M$. This phase diagram for the Bose-Fermi mixture is reminiscent of weakly attractive fermions with population imbalance, where the interacting fermions with opposite spins form singlet pairs.
We investigate the nature of trions, pairing and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the groundstate energy, critical fields, magnetization and phas
e diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.
We investigate the low temperature behaviour of the integrable 1D two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively af
fected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat $c_v sim T^{1/2}$ and the susceptibility $chi sim T^{-2}$ are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.
